\documentclass[9pt]{article}
\usepackage{amsmath}
\begin{document}
Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  -1.0 & -5.00 x_{1} & -4.00 x_{2} & +  9.00 x_{3} & -3.00 x_{4} & +  2.00 x_{5} & +  6.00 x_{6} & -2.00 x_{7} & +  7.00 x_{8}\\
 x_{10}   &  -1.0 & +  6.00 x_{1} & -1.00 x_{2} & +  7.00 x_{3} & -1.00 x_{4} & -8.00 x_{5} & -6.00 x_{6} &   & + 10.00 x_{8}\\
 x_{11}   &  -2.0 & +  4.00 x_{1} & +  2.00 x_{2} & +  1.00 x_{3} & +  9.00 x_{4} & + 10.00 x_{5} & + 10.00 x_{6} & + 10.00 x_{7} & -8.00 x_{8}\\
 x_{12}   &  1.0 & +  5.00 x_{1} & +  4.00 x_{2} & -10.00 x_{3} & +  5.00 x_{4} & +  5.00 x_{5} & +  1.00 x_{6} & +  1.00 x_{7} & -6.00 x_{8}\\
 x_{13}   &  3.0 & -7.00 x_{1} & +  2.00 x_{2} & -4.00 x_{3} & -7.00 x_{4} & -6.00 x_{5} & +  3.00 x_{6} & +  8.00 x_{7} & -8.00 x_{8}\\
 x_{14}   &  1.0 & +  1.00 x_{1} & +  2.00 x_{2} & -8.00 x_{3} & +  1.00 x_{4} & +  9.00 x_{5} & -4.00 x_{6} & + 10.00 x_{7} & +  5.00 x_{8}\\
 x_{15}   &  -2.0 & +  3.00 x_{1} & +  8.00 x_{2} & -9.00 x_{3} & +  8.00 x_{4} & -9.00 x_{5} & +  2.00 x_{6} & -4.00 x_{7} & -5.00 x_{8}\\
 x_{16}   &  0.0 & +  7.00 x_{1} & -8.00 x_{2} & -3.00 x_{3} & +  8.00 x_{4} & -5.00 x_{5} & +  4.00 x_{6} & +  7.00 x_{7} & -5.00 x_{8}\\
\hline
z    &  0.0 & -2.00 x_{1} & +  3.00 x_{2} & +  4.00 x_{3} & +  4.00 x_{4} & +  5.00 x_{5} & +  5.00 x_{6} & +  5.00 x_{7} & -2.00 x_{8}\\
\end{array}\]
\subsection{Initialization Phase: Dual Problem Solving}
New Objective in primal was changed to : \[ \max\ \sum_{j=1}^{8}\ - x_j \] 
Primal variable $x_j$ corresponds to dual variable $y_j$ for $j = 1,\ldots,16$
Dual Dictionary (with objective changed is): 
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.0 & +  5.00 y_{9} & -6.00 y_{10} & -4.00 y_{11} & -5.00 y_{12} & +  7.00 y_{13} & -1.00 y_{14} & -3.00 y_{15} & -7.00 y_{16}\\
 y_{2}   &  1.0 & +  4.00 y_{9} & +  1.00 y_{10} & -2.00 y_{11} & -4.00 y_{12} & -2.00 y_{13} & -2.00 y_{14} & -8.00 y_{15} & +  8.00 y_{16}\\
 y_{3}   &  1.0 & -9.00 y_{9} & -7.00 y_{10} & -1.00 y_{11} & + 10.00 y_{12} & +  4.00 y_{13} & +  8.00 y_{14} & +  9.00 y_{15} & +  3.00 y_{16}\\
 y_{4}   &  1.0 & +  3.00 y_{9} & +  1.00 y_{10} & -9.00 y_{11} & -5.00 y_{12} & +  7.00 y_{13} & -1.00 y_{14} & -8.00 y_{15} & -8.00 y_{16}\\
 y_{5}   &  1.0 & -2.00 y_{9} & +  8.00 y_{10} & -10.00 y_{11} & -5.00 y_{12} & +  6.00 y_{13} & -9.00 y_{14} & +  9.00 y_{15} & +  5.00 y_{16}\\
 y_{6}   &  1.0 & -6.00 y_{9} & +  6.00 y_{10} & -10.00 y_{11} & -1.00 y_{12} & -3.00 y_{13} & +  4.00 y_{14} & -2.00 y_{15} & -4.00 y_{16}\\
 y_{7}   &  1.0 & +  2.00 y_{9} &   & -10.00 y_{11} & -1.00 y_{12} & -8.00 y_{13} & -10.00 y_{14} & +  4.00 y_{15} & -7.00 y_{16}\\
 y_{8}   &  1.0 & -7.00 y_{9} & -10.00 y_{10} & +  8.00 y_{11} & +  6.00 y_{12} & +  8.00 y_{13} & -5.00 y_{14} & +  5.00 y_{15} & +  5.00 y_{16}\\
\hline
z    &  -0 & +  1.00 y_{9} & +  1.00 y_{10} & +  2.00 y_{11} & -1.00 y_{12} & -3.00 y_{13} & -1.00 y_{14} & +  2.00 y_{15} &   \\
\end{array}\]
Initialization succeeded in finding final dual dictionary with 12 pivots
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{3}   &  0.75003866976 & -8.57 y_{11} & +  0.75 y_{8} & +  0.20 y_{6} & +  2.56 y_{12} & -0.39 y_{2} & +  9.84 y_{14} & -0.31 y_{4} & +  0.70 y_{16}\\
 y_{13}   &  0.0202629543697 & +  0.73 y_{11} & -0.01 y_{8} & -0.01 y_{6} & +  0.14 y_{12} & -0.11 y_{2} & -0.11 y_{14} & +  0.11 y_{4} & +  1.81 y_{16}\\
 y_{9}   &  0.182366589327 & -0.43 y_{11} & -0.06 y_{8} & -0.10 y_{6} & +  0.24 y_{12} & -0.03 y_{2} & +  0.05 y_{14} & +  0.02 y_{4} & +  0.32 y_{16}\\
 y_{15}   &  0.223665893271 & -0.46 y_{11} & -0.04 y_{8} & -0.04 y_{6} & -0.37 y_{12} & -0.13 y_{2} & -0.29 y_{14} & -0.01 y_{4} & +  0.98 y_{16}\\
 y_{5}   &  3.57293116783 & +  2.66 y_{11} & -0.93 y_{8} & +  0.08 y_{6} & -5.12 y_{12} & -2.86 y_{2} & -18.52 y_{14} & +  1.13 y_{4} & + 41.85 y_{16}\\
 y_{1}   &  0.780355761794 & -8.33 y_{11} & +  0.24 y_{8} & -0.72 y_{6} & -3.85 y_{12} & +  0.22 y_{2} & +  4.00 y_{14} & +  0.48 y_{4} & -8.98 y_{16}\\
 y_{7}   &  2.09729311678 & -18.55 y_{11} & -0.23 y_{8} & -0.29 y_{6} & -3.09 y_{12} & +  0.33 y_{2} & -10.23 y_{14} & -0.91 y_{4} & -16.94 y_{16}\\
 y_{10}   &  0.100386697602 & +  1.45 y_{11} & -0.08 y_{8} & +  0.04 y_{6} & +  0.36 y_{12} & -0.13 y_{2} & -0.77 y_{14} & +  0.07 y_{4} & +  2.22 y_{16}\\
\hline
z    &  0.669296210363 & -0.10 y_{11} & -0.20 y_{8} & -0.12 y_{6} & -1.55 y_{12} & -0.08 y_{2} & -1.99 y_{14} & -0.27 y_{4} & -0.94 y_{16}\\
\end{array}\]
Primal Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{11}   &  0.0960556844548 & +  8.57 x_{3} & -0.73 x_{13} & +  0.43 x_{9} & +  0.46 x_{15} & -2.66 x_{5} & +  8.33 x_{1} & + 18.55 x_{7} & -1.45 x_{10}\\
 x_{8}   &  0.204485692189 & -0.75 x_{3} & +  0.01 x_{13} & +  0.06 x_{9} & +  0.04 x_{15} & +  0.93 x_{5} & -0.24 x_{1} & +  0.23 x_{7} & +  0.08 x_{10}\\
 x_{6}   &  0.116009280742 & -0.20 x_{3} & +  0.01 x_{13} & +  0.10 x_{9} & +  0.04 x_{15} & -0.08 x_{5} & +  0.72 x_{1} & +  0.29 x_{7} & -0.04 x_{10}\\
 x_{12}   &  1.55204949729 & -2.56 x_{3} & -0.14 x_{13} & -0.24 x_{9} & +  0.37 x_{15} & +  5.12 x_{5} & +  3.85 x_{1} & +  3.09 x_{7} & -0.36 x_{10}\\
 x_{2}   &  0.0810518174787 & +  0.39 x_{3} & +  0.11 x_{13} & +  0.03 x_{9} & +  0.13 x_{15} & +  2.86 x_{5} & -0.22 x_{1} & -0.33 x_{7} & +  0.13 x_{10}\\
 x_{14}   &  1.98824439288 & -9.84 x_{3} & +  0.11 x_{13} & -0.05 x_{9} & +  0.29 x_{15} & + 18.52 x_{5} & -4.00 x_{1} & + 10.23 x_{7} & +  0.77 x_{10}\\
 x_{4}   &  0.267749419954 & +  0.31 x_{3} & -0.11 x_{13} & -0.02 x_{9} & +  0.01 x_{15} & -1.13 x_{5} & -0.48 x_{1} & +  0.91 x_{7} & -0.07 x_{10}\\
 x_{16}   &  0.935189481825 & -0.70 x_{3} & -1.81 x_{13} & -0.32 x_{9} & -0.98 x_{15} & -41.85 x_{5} & +  8.98 x_{1} & + 16.94 x_{7} & -2.22 x_{10}\\
\hline
z    &  -0.669296210363 & -0.75 x_{3} & -0.02 x_{13} & -0.18 x_{9} & -0.22 x_{15} & -3.57 x_{5} & -0.78 x_{1} & -2.10 x_{7} & -0.10 x_{10}\\
\end{array}\]
Primal Dictionary with original objective is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{11}   &  0.0960556844548 & +  8.57 x_{3} & -0.73 x_{13} & +  0.43 x_{9} & +  0.46 x_{15} & -2.66 x_{5} & +  8.33 x_{1} & + 18.55 x_{7} & -1.45 x_{10}\\
 x_{8}   &  0.204485692189 & -0.75 x_{3} & +  0.01 x_{13} & +  0.06 x_{9} & +  0.04 x_{15} & +  0.93 x_{5} & -0.24 x_{1} & +  0.23 x_{7} & +  0.08 x_{10}\\
 x_{6}   &  0.116009280742 & -0.20 x_{3} & +  0.01 x_{13} & +  0.10 x_{9} & +  0.04 x_{15} & -0.08 x_{5} & +  0.72 x_{1} & +  0.29 x_{7} & -0.04 x_{10}\\
 x_{12}   &  1.55204949729 & -2.56 x_{3} & -0.14 x_{13} & -0.24 x_{9} & +  0.37 x_{15} & +  5.12 x_{5} & +  3.85 x_{1} & +  3.09 x_{7} & -0.36 x_{10}\\
 x_{2}   &  0.0810518174787 & +  0.39 x_{3} & +  0.11 x_{13} & +  0.03 x_{9} & +  0.13 x_{15} & +  2.86 x_{5} & -0.22 x_{1} & -0.33 x_{7} & +  0.13 x_{10}\\
 x_{14}   &  1.98824439288 & -9.84 x_{3} & +  0.11 x_{13} & -0.05 x_{9} & +  0.29 x_{15} & + 18.52 x_{5} & -4.00 x_{1} & + 10.23 x_{7} & +  0.77 x_{10}\\
 x_{4}   &  0.267749419954 & +  0.31 x_{3} & -0.11 x_{13} & -0.02 x_{9} & +  0.01 x_{15} & -1.13 x_{5} & -0.48 x_{1} & +  0.91 x_{7} & -0.07 x_{10}\\
 x_{16}   &  0.935189481825 & -0.70 x_{3} & -1.81 x_{13} & -0.32 x_{9} & -0.98 x_{15} & -41.85 x_{5} & +  8.98 x_{1} & + 16.94 x_{7} & -2.22 x_{10}\\
\hline
z    &  1.48522815159 & +  6.91 x_{3} & -0.06 x_{13} & +  0.42 x_{9} & +  0.57 x_{15} & +  6.80 x_{5} & -0.51 x_{1} & +  8.62 x_{7} & -0.26 x_{10}\\
\end{array}\]
\section{Optimization Phase Simplex}
Starting Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{11}   &  0.0960556844548 & +  8.57 x_{3} & -0.73 x_{13} & +  0.43 x_{9} & +  0.46 x_{15} & -2.66 x_{5} & +  8.33 x_{1} & + 18.55 x_{7} & -1.45 x_{10}\\
 x_{8}   &  0.204485692189 & -0.75 x_{3} & +  0.01 x_{13} & +  0.06 x_{9} & +  0.04 x_{15} & +  0.93 x_{5} & -0.24 x_{1} & +  0.23 x_{7} & +  0.08 x_{10}\\
 x_{6}   &  0.116009280742 & -0.20 x_{3} & +  0.01 x_{13} & +  0.10 x_{9} & +  0.04 x_{15} & -0.08 x_{5} & +  0.72 x_{1} & +  0.29 x_{7} & -0.04 x_{10}\\
 x_{12}   &  1.55204949729 & -2.56 x_{3} & -0.14 x_{13} & -0.24 x_{9} & +  0.37 x_{15} & +  5.12 x_{5} & +  3.85 x_{1} & +  3.09 x_{7} & -0.36 x_{10}\\
 x_{2}   &  0.0810518174787 & +  0.39 x_{3} & +  0.11 x_{13} & +  0.03 x_{9} & +  0.13 x_{15} & +  2.86 x_{5} & -0.22 x_{1} & -0.33 x_{7} & +  0.13 x_{10}\\
 x_{14}   &  1.98824439288 & -9.84 x_{3} & +  0.11 x_{13} & -0.05 x_{9} & +  0.29 x_{15} & + 18.52 x_{5} & -4.00 x_{1} & + 10.23 x_{7} & +  0.77 x_{10}\\
 x_{4}   &  0.267749419954 & +  0.31 x_{3} & -0.11 x_{13} & -0.02 x_{9} & +  0.01 x_{15} & -1.13 x_{5} & -0.48 x_{1} & +  0.91 x_{7} & -0.07 x_{10}\\
 x_{16}   &  0.935189481825 & -0.70 x_{3} & -1.81 x_{13} & -0.32 x_{9} & -0.98 x_{15} & -41.85 x_{5} & +  8.98 x_{1} & + 16.94 x_{7} & -2.22 x_{10}\\
\hline
z    &  1.48522815159 & +  6.91 x_{3} & -0.06 x_{13} & +  0.42 x_{9} & +  0.57 x_{15} & +  6.80 x_{5} & -0.51 x_{1} & +  8.62 x_{7} & -0.26 x_{10}\\
\end{array}\]


 $ x_{3} $ enters and $ x_{14} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{11}   &  1.82810314754 & -0.87 x_{14} & -0.64 x_{13} & +  0.38 x_{9} & +  0.72 x_{15} & + 13.47 x_{5} & +  4.85 x_{1} & + 27.47 x_{7} & -0.78 x_{10}\\
 x_{8}   &  0.0526109024624 & +  0.08 x_{14} & -0.00 x_{13} & +  0.07 x_{9} & +  0.02 x_{15} & -0.49 x_{5} & +  0.07 x_{1} & -0.55 x_{7} & +  0.02 x_{10}\\
 x_{6}   &  0.0747678237503 & +  0.02 x_{14} & +  0.01 x_{13} & +  0.11 x_{9} & +  0.04 x_{15} & -0.46 x_{5} & +  0.80 x_{1} & +  0.08 x_{7} & -0.06 x_{10}\\
 x_{12}   &  1.03584392728 & +  0.26 x_{14} & -0.17 x_{13} & -0.23 x_{9} & +  0.29 x_{15} & +  0.32 x_{5} & +  4.89 x_{1} & +  0.44 x_{7} & -0.56 x_{10}\\
 x_{2}   &  0.160504109245 & -0.04 x_{14} & +  0.12 x_{13} & +  0.03 x_{9} & +  0.14 x_{15} & +  3.60 x_{5} & -0.38 x_{1} & +  0.07 x_{7} & +  0.16 x_{10}\\
 x_{3}   &  0.201989408677 & -0.10 x_{14} & +  0.01 x_{13} & -0.01 x_{9} & +  0.03 x_{15} & +  1.88 x_{5} & -0.41 x_{1} & +  1.04 x_{7} & +  0.08 x_{10}\\
 x_{4}   &  0.330923833619 & -0.03 x_{14} & -0.11 x_{13} & -0.02 x_{9} & +  0.02 x_{15} & -0.54 x_{5} & -0.61 x_{1} & +  1.23 x_{7} & -0.05 x_{10}\\
 x_{16}   &  0.793406351651 & +  0.07 x_{14} & -1.82 x_{13} & -0.31 x_{9} & -1.00 x_{15} & -43.17 x_{5} & +  9.27 x_{1} & + 16.21 x_{7} & -2.27 x_{10}\\
\hline
z    &  2.88178261075 & -0.70 x_{14} & +  0.01 x_{13} & +  0.38 x_{9} & +  0.77 x_{15} & + 19.81 x_{5} & -3.32 x_{1} & + 15.81 x_{7} & +  0.28 x_{10}\\
\end{array}\]


 $ x_{5} $ enters and $ x_{16} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{11}   &  2.07571113425 & -0.85 x_{14} & -1.21 x_{13} & +  0.28 x_{9} & +  0.41 x_{15} & -0.31 x_{16} & +  7.74 x_{1} & + 32.52 x_{7} & -1.49 x_{10}\\
 x_{8}   &  0.0436400171823 & +  0.08 x_{14} & +  0.02 x_{13} & +  0.07 x_{9} & +  0.03 x_{15} & +  0.01 x_{16} & -0.04 x_{1} & -0.73 x_{7} & +  0.05 x_{10}\\
 x_{6}   &  0.0663009370154 & +  0.02 x_{14} & +  0.03 x_{13} & +  0.11 x_{9} & +  0.05 x_{15} & +  0.01 x_{16} & +  0.71 x_{1} & -0.09 x_{7} & -0.03 x_{10}\\
 x_{12}   &  1.04167789095 & +  0.26 x_{14} & -0.18 x_{13} & -0.23 x_{9} & +  0.28 x_{15} & -0.01 x_{16} & +  4.95 x_{1} & +  0.56 x_{7} & -0.57 x_{10}\\
 x_{2}   &  0.226594637098 & -0.03 x_{14} & -0.03 x_{13} & +  0.00 x_{9} & +  0.06 x_{15} & -0.08 x_{16} & +  0.39 x_{1} & +  1.42 x_{7} & -0.03 x_{10}\\
 x_{3}   &  0.236565441824 & -0.10 x_{14} & -0.07 x_{13} & -0.02 x_{9} & -0.01 x_{15} & -0.04 x_{16} & -0.00 x_{1} & +  1.75 x_{7} & -0.02 x_{10}\\
 x_{4}   &  0.32091866823 & -0.03 x_{14} & -0.09 x_{13} & -0.02 x_{9} & +  0.03 x_{15} & +  0.01 x_{16} & -0.73 x_{1} & +  1.03 x_{7} & -0.02 x_{10}\\
 x_{5}   &  0.0183799171466 & +  0.00 x_{14} & -0.04 x_{13} & -0.01 x_{9} & -0.02 x_{15} & -0.02 x_{16} & +  0.21 x_{1} & +  0.38 x_{7} & -0.05 x_{10}\\
\hline
z    &  3.24584458795 & -0.67 x_{14} & -0.83 x_{13} & +  0.24 x_{9} & +  0.31 x_{15} & -0.46 x_{16} & +  0.93 x_{1} & + 23.24 x_{7} & -0.76 x_{10}\\
\end{array}\]


 $ x_{1} $ enters and $ x_{4} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{11}   &  5.49397065146 & -1.20 x_{14} & -2.13 x_{13} & +  0.11 x_{9} & +  0.75 x_{15} & -0.18 x_{16} & -10.65 x_{4} & + 43.47 x_{7} & -1.70 x_{10}\\
 x_{8}   &  0.0273893667405 & +  0.08 x_{14} & +  0.02 x_{13} & +  0.07 x_{9} & +  0.03 x_{15} & +  0.01 x_{16} & +  0.05 x_{4} & -0.78 x_{7} & +  0.05 x_{10}\\
 x_{6}   &  0.377991499886 & -0.01 x_{14} & -0.06 x_{13} & +  0.09 x_{9} & +  0.08 x_{15} & +  0.02 x_{16} & -0.97 x_{4} & +  0.91 x_{7} & -0.05 x_{10}\\
 x_{12}   &  3.23028674105 & +  0.04 x_{14} & -0.77 x_{13} & -0.35 x_{9} & +  0.50 x_{15} & +  0.08 x_{16} & -6.82 x_{4} & +  7.56 x_{7} & -0.70 x_{10}\\
 x_{2}   &  0.399306923053 & -0.05 x_{14} & -0.08 x_{13} & -0.00 x_{9} & +  0.07 x_{15} & -0.08 x_{16} & -0.54 x_{4} & +  1.98 x_{7} & -0.04 x_{10}\\
 x_{3}   &  0.235528912112 & -0.10 x_{14} & -0.07 x_{13} & -0.02 x_{9} & -0.01 x_{15} & -0.04 x_{16} & +  0.00 x_{4} & +  1.74 x_{7} & -0.02 x_{10}\\
 x_{1}   &  0.441726318785 & -0.04 x_{14} & -0.12 x_{13} & -0.02 x_{9} & +  0.04 x_{15} & +  0.02 x_{16} & -1.38 x_{4} & +  1.41 x_{7} & -0.03 x_{10}\\
 x_{5}   &  0.113212255316 & -0.01 x_{14} & -0.07 x_{13} & -0.01 x_{9} & -0.01 x_{15} & -0.02 x_{16} & -0.30 x_{4} & +  0.68 x_{7} & -0.06 x_{10}\\
\hline
z    &  3.65782382257 & -0.71 x_{14} & -0.94 x_{13} & +  0.22 x_{9} & +  0.35 x_{15} & -0.44 x_{16} & -1.28 x_{4} & + 24.56 x_{7} & -0.79 x_{10}\\
\end{array}\]


 $ x_{7} $ enters and $ x_{8} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{11}   &  7.01220929601 & +  3.08 x_{14} & -0.80 x_{13} & +  4.11 x_{9} & +  2.28 x_{15} & +  0.41 x_{16} & -7.84 x_{4} & -55.43 x_{8} & +  1.03 x_{10}\\
 x_{7}   &  0.0349269697777 & +  0.10 x_{14} & +  0.03 x_{13} & +  0.09 x_{9} & +  0.04 x_{15} & +  0.01 x_{16} & +  0.06 x_{4} & -1.28 x_{8} & +  0.06 x_{10}\\
 x_{6}   &  0.409603734608 & +  0.08 x_{14} & -0.03 x_{13} & +  0.18 x_{9} & +  0.11 x_{15} & +  0.04 x_{16} & -0.91 x_{4} & -1.15 x_{8} & +  0.00 x_{10}\\
 x_{12}   &  3.49441770386 & +  0.78 x_{14} & -0.54 x_{13} & +  0.35 x_{9} & +  0.77 x_{15} & +  0.18 x_{16} & -6.33 x_{4} & -9.64 x_{8} & -0.23 x_{10}\\
 x_{2}   &  0.468369757392 & +  0.14 x_{14} & -0.02 x_{13} & +  0.18 x_{9} & +  0.14 x_{15} & -0.05 x_{16} & -0.41 x_{4} & -2.52 x_{8} & +  0.09 x_{10}\\
 x_{3}   &  0.296384686113 & +  0.07 x_{14} & -0.01 x_{13} & +  0.14 x_{9} & +  0.05 x_{15} & -0.02 x_{16} & +  0.12 x_{4} & -2.22 x_{8} & +  0.09 x_{10}\\
 x_{1}   &  0.491121935136 & +  0.09 x_{14} & -0.08 x_{13} & +  0.11 x_{9} & +  0.09 x_{15} & +  0.04 x_{16} & -1.29 x_{4} & -1.80 x_{8} & +  0.06 x_{10}\\
 x_{5}   &  0.136929031071 & +  0.06 x_{14} & -0.05 x_{13} & +  0.05 x_{9} & +  0.01 x_{15} & -0.01 x_{16} & -0.25 x_{4} & -0.87 x_{8} & -0.02 x_{10}\\
\hline
z    &  4.51570282364 & +  1.71 x_{14} & -0.18 x_{13} & +  2.48 x_{9} & +  1.22 x_{15} & -0.11 x_{16} & +  0.30 x_{4} & -31.32 x_{8} & +  0.75 x_{10}\\
\end{array}\]


 $ x_{4} $ enters and $ x_{1} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{11}   &  4.01433728111 & +  2.51 x_{14} & -0.33 x_{13} & +  3.46 x_{9} & +  1.71 x_{15} & +  0.19 x_{16} & +  6.10 x_{1} & -44.42 x_{8} & +  0.65 x_{10}\\
 x_{7}   &  0.0596044270756 & +  0.10 x_{14} & +  0.03 x_{13} & +  0.10 x_{9} & +  0.04 x_{15} & +  0.02 x_{16} & -0.05 x_{1} & -1.37 x_{8} & +  0.07 x_{10}\\
 x_{6}   &  0.0607678768533 & +  0.01 x_{14} & +  0.03 x_{13} & +  0.10 x_{9} & +  0.04 x_{15} & +  0.01 x_{16} & +  0.71 x_{1} & +  0.13 x_{8} & -0.04 x_{10}\\
 x_{12}   &  1.07477103905 & +  0.32 x_{14} & -0.16 x_{13} & -0.18 x_{9} & +  0.31 x_{15} & +  0.00 x_{16} & +  4.93 x_{1} & -0.76 x_{8} & -0.54 x_{10}\\
 x_{2}   &  0.311494287163 & +  0.11 x_{14} & +  0.01 x_{13} & +  0.14 x_{9} & +  0.11 x_{15} & -0.06 x_{16} & +  0.32 x_{1} & -1.95 x_{8} & +  0.07 x_{10}\\
 x_{3}   &  0.340616330062 & +  0.08 x_{14} & -0.02 x_{13} & +  0.15 x_{9} & +  0.06 x_{15} & -0.02 x_{16} & -0.09 x_{1} & -2.38 x_{8} & +  0.09 x_{10}\\
 x_{4}   &  0.382160436741 & +  0.07 x_{14} & -0.06 x_{13} & +  0.08 x_{9} & +  0.07 x_{15} & +  0.03 x_{16} & -0.78 x_{1} & -1.40 x_{8} & +  0.05 x_{10}\\
 x_{5}   &  0.040756540676 & +  0.04 x_{14} & -0.03 x_{13} & +  0.03 x_{9} & -0.01 x_{15} & -0.02 x_{16} & +  0.20 x_{1} & -0.51 x_{8} & -0.03 x_{10}\\
\hline
z    &  4.63123415173 & +  1.73 x_{14} & -0.20 x_{13} & +  2.51 x_{9} & +  1.24 x_{15} & -0.10 x_{16} & -0.24 x_{1} & -31.75 x_{8} & +  0.76 x_{10}\\
\end{array}\]


 $ x_{9} $ enters and $ x_{12} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{11}   &  24.8801628789 & +  8.67 x_{14} & -3.52 x_{13} & -19.41 x_{12} & +  7.66 x_{15} & +  0.21 x_{16} & + 101.75 x_{1} & -59.15 x_{8} & -9.75 x_{10}\\
 x_{7}   &  0.648428843744 & +  0.28 x_{14} & -0.06 x_{13} & -0.55 x_{12} & +  0.21 x_{15} & +  0.02 x_{16} & +  2.65 x_{1} & -1.78 x_{8} & -0.23 x_{10}\\
 x_{6}   &  0.662595624374 & +  0.19 x_{14} & -0.07 x_{13} & -0.56 x_{12} & +  0.22 x_{15} & +  0.01 x_{16} & +  3.47 x_{1} & -0.30 x_{8} & -0.34 x_{10}\\
 x_{9}   &  6.03300558466 & +  1.78 x_{14} & -0.92 x_{13} & -5.61 x_{12} & +  1.72 x_{15} & +  0.01 x_{16} & + 27.66 x_{1} & -4.26 x_{8} & -3.01 x_{10}\\
 x_{2}   &  1.1786169806 & +  0.37 x_{14} & -0.13 x_{13} & -0.81 x_{12} & +  0.36 x_{15} & -0.06 x_{16} & +  4.29 x_{1} & -2.56 x_{8} & -0.36 x_{10}\\
 x_{3}   &  1.25477598569 & +  0.35 x_{14} & -0.16 x_{13} & -0.85 x_{12} & +  0.32 x_{15} & -0.02 x_{16} & +  4.10 x_{1} & -3.03 x_{8} & -0.36 x_{10}\\
 x_{4}   &  0.886626681887 & +  0.22 x_{14} & -0.14 x_{13} & -0.47 x_{12} & +  0.22 x_{15} & +  0.03 x_{16} & +  1.53 x_{1} & -1.76 x_{8} & -0.20 x_{10}\\
 x_{5}   &  0.217826811386 & +  0.09 x_{14} & -0.06 x_{13} & -0.16 x_{12} & +  0.04 x_{15} & -0.02 x_{16} & +  1.01 x_{1} & -0.64 x_{8} & -0.12 x_{10}\\
\hline
z    &  19.7457180096 & +  6.19 x_{14} & -2.51 x_{13} & -14.06 x_{12} & +  5.56 x_{15} & -0.08 x_{16} & + 69.05 x_{1} & -42.41 x_{8} & -6.76 x_{10}\\
\end{array}\]


 $ x_{1} $ enters and Unbounded Dictionary!


 $ x_{1} $ enters and Unbounded Dictionary!
\end{document}
